Method and Apparatus for Optical Phase Modulation

ABSTRACT

A method of phase modulating optical radiation by the steps of phase modulating the optical radiation by using a modulator having an extinction ratio in order to provide a multilevel phase shift key signal, and applying to each optical pulse a phase-shift having an absolute value depending on the extinction ratio and a sign depending, for each of the optical pulses, on the respective optical phase value. An apparatus implementing the method is also disclosed.

The present invention generally relates to a method and apparatus foroptical phase modulation for use in the field of opticaltelecommunication systems, in particular to a method and apparatus usingthe multi-level phase shift key (MPSK) modulation technique.

Currently deployed optical telecommunication systems make mostly use ofbinary on-off key (OOK) modulation format with direct detection at thereceiver (OOK/DD). In the art, OOK/DD is also referred to as (binary)intensity modulation with direct detection (IM/DD). By modulating theoptical intensity, a binary-digital information signal is encoded in acorresponding binary-digital optical signal consisting of a stream ofoptical pulses. Usually, in OOK/DD format a logical binary digit (bit)“1” is associated to a first level of optical intensity in a time slotof the optical stream, while a logical bit “0” is associated to a secondlevel of optical intensity different from the first level. The time slotcorresponding to a single bit (both 1 or 0) is known as bit-period T [s]and the optical pulse stream is characterized by an optical rate B=1/T[s⁻¹]. In OOK/DD, the rate B of the optical signal is equal to thebit-rate of the encoded digital information and both are thus expressedin [bit/s] units. Exemplary optical bit-rates are 2.5, 10, 40 and 160Gbit/s.

In the art, a general distinction is done between return to zero (RZ)and non-return to zero (NRZ) transmission. Independently from themodulation format, in RZ transmission the optical intensity of theoptical signal always goes to a low intensity level between two adjacentpulses, while this does not happen in NRZ transmission. For the purposeof the present invention, “optical pulse”, or equivalently “opticalsymbol”, shall indicate the transmitted optical field, which solelyoccupies the time slot, or symbol-period, T and constitutes theelementary part of the transmitted optical stream, independently fromthe fact that the streamed optical field is pulsed or continuous.

In an attempt of increasing capacity of the optical telecommunicationsystems, modulation formats alternative to binary on-off key have beeninvestigated. Among the alternative modulation formats, some phase shiftkey (PSK) techniques are particularly promising. These techniques encodeinformation by modulating the optical phase of the carrier between adiscrete set of M predetermined values. For example binary (M=2) phaseshift key technique (BPSK) encodes a single bit in a time slot T byapplying to the optical field in the time slot one phase value out oftwo predetermined phase values, which typically differ by π radians (0,π). Advantageously, M=2^(N) in order to encode N bits of information ineach transmitted optical symbol which is in a symbol-period T(multi-level or M-ary phase shift key—MPSK). The optical symbol rateB=1/T is expressed in [symbol/s] and the total transmission capacity[bit/s] is obtained by multiplying B by N. For example, in quaternaryphase shift keying M=4 (N=2), the four phase symbols are typically in aquadrature constellation (quadrature phase shift keying—QPSK), as shownin FIG. 1. Here, X₁, X₂ is the phase symbol space and the depicted phasesymbol values (+π/4, +3/4π, +5/4π, −π/4) are arbitrary. The choice of areference system is arbitrary as it depends on the absolute opticalfield phase, which is a priori unknown. The modulation format ischaracterized by the distance between symbols. Thus any quadratureconstellation may be arbitrarily chosen by rotation of the one depicted.For the purpose of the present invention, the term “MPSK”, or“multi-level phase shift keying”, will be referred to modulation formatshaving M greater than 2.

In optical differential multi-level phase shift key (DMPSK) techniques,information is encoded in the differential optical phase associated tosuccessive symbols. For example, in DQPSK the four values of the opticalphase differences between adjacent pulses are 0, +π/2, +π and +3/2π.Typically, a digital pre-coder is used to differentially encode twobinary data streams each at a bit rate B [bit/s] and the resultingencoded signals are subsequently fed to an optical modulator so that asingle transmitted optical stream at the same symbol rate B [symbol/s]is obtained. Decoding can be performed optically without the employmentof a coherent local oscillator, by using a pair of unbalancedMach-Zehnder interferometers (MZI). Advantageously, each MZI has one armdimensioned in order to introduce an optical time delay equal to onesymbol period with respect to the other arm. By setting the differentialoptical phase between the interferometer arms respectively to +π/4 and−π/4 and by employing balanced optical detectors (also known asdifferential photoreceiver) at the output of each interferometer, theDQPSK signal is converted back into two binary intensity sequences whichrepresent the two original data streams at B [bit/s].

For each MZI, the output current I_(out) after the balancedphotodetector is proportional to: $\begin{matrix}{{I_{out} \div \frac{I_{in}}{2}}{\cos\left( {\Delta \pm \frac{\pi}{4}} \right)}} & (1)\end{matrix}$

where I_(in) is the input optical intensity into the MZI, Δ is thereceived phase difference between adjacent pulses and the sign plus orminus holds for MZI having differential optical phase between theinterferometer arms equal to +π/4 and −π/4, respectively.

In order to perform a QPSK modulation, it has been proposed the use of asingle phase-modulator driven by a four-level electrical input voltagein order to directly obtain the required four output phase levels. Thissolution has the disadvantage that commercially availablephase-modulators need very high drive voltages V_(π). Besides that, itis necessary to drive the modulator with a voltage able to generate a 0to 3/2π phase swing, feeding the modulator with more than V_(π), thusincreasing drive electronics costs. In general, the “drive voltage”,V_(π), of a phase shifter is defined as the voltage which produces aphase shift of π at the optical carrier frequency.

Alternatively, it is known in the art the use of a cascade of two phaseshifters, the first one producing a 0-π modulation, the second one a0-π/2 modulation, or vice versa. Typically, a push-pull Mach-ZehnderModulator (MZM) biased at the zero point and driven at a voltage equalto double the π voltage, V_(π), is used to apply the π-depth phasemodulation. In case of a MZM, the π voltage, V_(π), is defined as thevoltage which produces a phase shift difference between the first andsecond arm of π. A phase modulator consisting of a single waveguide withone electrode driven at half the π voltage may be used to apply theπ/2-depth phase modulation.

In patent application WO 03/049331 it is disclosed a method andapparatus for encoding an optical signal having improved dispersiontolerance in a WDM optical communications system. There is provided aDQPSK modulator arrangement comprising a laser for producing an opticalsignal, which signal is split by a splitter, each part of the splitsignal being applied to a respective phase modulator, exemplarily a MZM.Each phase modulator is adapted to modulate the phase of the signal by 0or π radians in dependence upon a respective drive voltage. The opticaloutput of at least one modulator is passed through a phase shifter whichapplies a phase shift of π/2, such that the relative phase differencebetween the two parts of the split optical signals is ±π/2. A controlelectrode is used to provide the fine control. The split signals arerecombined by an optical recombiner to form an optical PSK output. Afurther phase modulator is provided after the recombiner to chirp theoptical PSK output Exemplarily, the further phase modulator applies aπ/4 phase modulation to the output signal and it is driven by anoscillator which provides the clock rate corresponding to the data linerate. The oscillator must be synchronous with the data clock rate, i.e.it should be phase locked with the data stream.

Chirping relates to the variation of an optical signal's phasemodulation, i.e. the optical phase is changed continuously within thesymbol period in order to improve dispersion tolerance.

A generic interferometric modulator, such as for example a MZM, has anassociated “extinction ratio” (“ER”) which is defined as the ratiobetween maximum and minimum optical intensity at the output of themodulator when operated in intensity modulation. Such extinction ratiotypically depends not only on splitting ratios of input and outputcouplers of the interferometer but also on the rate at which themodulator is operated. For the purpose of the present invention, “RadioFrequency extinction ratio” (“RF-ER”) means the ER measured at highfrequency modulation rate, i.e. higher than 1 Gbit/s, typically higheror equal than about 2.5 Gbit/s. For example, MZMs having two electrodesdriven independently, known in the market as dual-drive MZMs (DD-MZM),typically show a Radio Frequency modulation ER which ranges betweenabout 11 to 15 dB.

Applicant has found that a finite value of the ER of a modulator affectsthe MPSK optical signal emitted by the modulator with a phase errordepending on the value of the ER.

For the purpose of the present invention, we will refer to a “non-ideal”or “finite” ER as a RF-ER equal to or less than about 30 dB. An “ideal”ER means a RF-ER greater than about 30 dB.

The Applicant has faced the problem of modulating an optical radiationin a multi-level phase shift key format while reducing the error in thephase of the transmitted optical symbols to an acceptable value. Inparticular, Applicant has faced the problem of reducing the opticalphase error in a MPSK modulated signal due to the extinction ratio ofthe modulator employed for MPSK modulation. The Applicant has verifiedthat the above problems are particularly relevant in the differentialmultilevel phase shift keying transmission, more particularly in thedifferential multilevel phase shift keying transmission employing adual-drive MZM, and a need for better quality optical modulation istherefore strongly felt in these applications.

Applicant has found a solution to the problem of generating a properMPSK signal by modulation, also in presence of a non-ideal ER of themodulator, while avoiding detrimental amplitude modulation.

The Applicant has found that it is possible to suitably reduce the phaseerror induced by the ER of an interferometric MPSK modulator by placinga phase shifter at the output end of the modulator and driving the phaseshifter by a proper algorithm.

Advantageously, the phase shifter applies to the MPSK signal a phaseshift which is substantially constant along the symbol-period. Theapplied phase shift has an absolute value which is a function of the ERof the modulator, preferably decreasing with increasing ER, morepreferably inversely proportional to ER. Preferably, the sign of thephase-shift is determined on a symbol-by-symbol basis, in dependence onthe phase-symbol value of each symbol. A proper algorithm decides theright sign of the phase-shift and feeds the phase shifter driver.

The present invention allows relaxing the ER requirements in MZMfabrication and, for example, makes possible the use of a commerciallyavailable DD-MZM for MPSK modulation. The solution is simple andcost-effective, in that it relaxes constraints in the design of the MZM.In particular, splitting ratios of the couplers included in the MZI donot need to be necessarily close to the ideal 3 dB value. Furthermore,there is no need to precisely balance interferometer arm losses.

In a first aspect, the invention relates to a method for modulating anoptical radiation, the method comprising the steps of phase-modulatingan optical radiation with a modulation signal, by using a modulatorhaving an extinction ratio, so as to obtain a multi-level phase shiftkey optical signal including a stream of optical pulses, wherein each ofsaid optical pulses has a respective optical phase value related to saidmodulation signal and applying to each of said optical pulses aphase-shift having an absolute value related to said extinction ratioand a sign related, for each of the optical pulses, to said respectiveoptical phase value. Preferably the phase-shift is substantiallyconstant in each of said optical pulses. Advantageously the absolutevalue of said phase-shift is equal to or less than about π/10.

More preferably, the absolute value of said phase-shift is determined asa function of said extinction ratio, said function being a decreasingfunction with increasing of extinction ratio, for example according tothe approximate relation${{arc}\quad{{tg}\left( \frac{1}{{ER}_{lin}} \right)}},$wherein ER_(lin) is the extinction ratio.

The method of the present invention may further comprise the steps ofproviding a first and a second logical signal (S₁, S₂) linked with saidmodulation signal, generating a first and a second driving signal forsaid modulator from said first and second logical signal andestablishing said sign as a logical function of said logical signals,for example through a logical relation equivalent to NOT[XOR(S₁,S₂)].

The multilevel phase shift key optical signal can be a quadrature phaseshift key optical signal or a differential multilevel phase shift keyoptical signal.

In a second aspect, the invention relates to a method of opticalcommunication comprising transmitting an optical signal at a firstlocation and receiving the optical signal at a second location differentfrom the first location, wherein transmitting comprises modulating theoptical signal according to the method above.

In a third aspect, the invention relates to an electro-optical apparatusfor modulating an optical radiation based on a modulation signal,comprising an optical modulator apt to receiving an optical radiationand generating a multilevel phase shift key optical signal including astream of optical pulses, each having a respective optical phase valuerelated to said modulation signal, said optical modulator having anextinction ratio and being apt to being driven by a first and a seconddriving signal and a phase-shifter optically connected to the opticalmodulator, apt to applying to the phase of each optical pulse aphase-shift having an absolute value related to said extinction ratioand a sign depending, for each of the optical pulses, on said respectiveoptical phase value; and a logical circuit apt to generating a thirddriving signal logically related to said first and second drivingsignals, the logical circuit being logically connected to thephase-shifter for feeding said third driving signal to saidphase-shifter.

Preferably, the third driving signal determines said sign of said phaseshift.

The optical modulator may comprise a dual-drive Mach-Zehnder modulator.

The optical modulator is advantageously an optical modulator apt toreceiving an optical radiation and generating a quadrature phase shiftkey optical signal.

In a fourth aspect, the invention relates to an optical transmittercomprising an optical source optically coupled to the electro-opticalapparatus described above.

In a fifth aspect, the invention relates to an optical communicationsystem comprising an optical transmitter for transmitting an opticalsignal, an optical receiver for receiving the optical signal, and anoptical communication line connecting the transmitter to the receiver,wherein the transmitter comprises the apparatus described above.

The features and advantages of the present invention will be madeapparent by the following detailed description of some exemplaryembodiments thereof, provided merely by way of non-limitative examples,description that will be conducted by making reference to the attacheddrawings, wherein:

FIG. 1 shows a symbolic diagram of a particular QPSK constellation

FIG. 2 shows a schematic diagram of an exemplary optical deviceaccording to the invention;

FIG. 3 shows a perturbation of the QPSK constellation of FIG. 1 due tonon-ideal (finite ER) MZM modulation.

FIG. 4 a and 4 b show an output current after the differentialphotodetector with the original and the distorted constellation,respectively;

FIG. 5 shows an exemplary logic circuit implementing the sign of thephase correction;

FIG. 6 a and 6 b show simulated eye diagrams of a NRZ DQPSK signal at 10Gbit/s generated by a DD-MZM transmitter with ER=20 dB before and afterphase correction, respectively;

FIG. 7 a and 7 b show simulated eye diagrams of a NRZ DQPSK signal at 10Gbit/s generated by a DD-MZM transmitter with ER=15 dB before and afterphase correction, respectively;

FIG. 8 a and 8 b show simulated eye diagrams of a NRZ DQPSK signal at 10Gbit/s generated by a DD-MZM transmitter with ER=12 dB before and afterphase correction, respectively;

FIG. 2 shows an exemplary optical device 10 according to a particularembodiment of the invention.

The device comprises an optical modulator 20, a phase shifter 40optically connected to the modulator 20 and a logical circuit 50.

The optical modulator 20 comprises an optical input 21 and an opticaloutput 22. Typically, the modulator 20 has a first driving input 23 anda second driving input 24. A first driver 30 and a second 31 driver 31are connected to respectively the first and second driving input 23, 24.A first signal transmitting line 32 and a second signal transmittingline 33 are connected to the input of first and second driver 30,31respectively.

Modulator 20 may be any kind of MPSK modulator. Advantageously, it maycomprise an interferometric modulator 60 such as, for example, a MZM.The MZM has an optical divider 61, an optical combiner 62, a firstoptical arm 63 and a second optical arm 64 arranged in parallel betweenthe optical divider 61 and the optical combiner 62. The MZM 60advantageously comprises a first phase-shifting device 65 and a secondphase-shifting device 66 acting respectively on the first and secondoptical arm 63,64 for changing the optical phase of an optical radiationtraveling respectively in the first and second optical arm 63,64.Phase-shifting devices 65 and 66 may be any kind of optical phaseshifter or phase modulator, such as for example MZM (either singledrive, push-pull or dual-drive MZM). In this case the modulator 60 takesthe form of a MZ super-structure having a pair of MZM in parallelconfiguration. In a more preferred configuration phase-shifting devices65 and 66 are electrodes (e.g. traveling wave electrodes) associated tothe optical arms 63 and 64. In this latter preferred configuration, themodulator 60 is known in the art as a (symmetric) dual-drive MZM(DD-MZM).

An optical phase-shifting device 40 is optically connected, e.g. by asuitable waveguide such as a planar waveguide or an optical fiber, tothe output 22 of the modulator 20, advantageously in a downstreamposition with respect to the direction of propagation of an opticalradiation. Such device 40 may be a phase modulator or a phase shifter.Preferably the phase shifting device 40 comprises an electrode 42associated to a waveguide 41 through which the optical signalpropagates. For example it may be a traveling wave integrated opticalphase modulator. Typically, the device 40 has a driving input 43. Adriver 44 is connected to the driving input 43.

A logical circuit 50 has a logical output 53 associated to the driver44, for example by way of a signal transmitting line 56. In a particularconfiguration, the logical circuit has a first logical input 51 and asecond logical input 52. Preferably, a first signal transmitting line 54and a second signal transmitting line 55 are connected to the first andsecond logical input, respectively. Optionally, a pair of splittingdevices 57 provides a connection between signal transmitting line 32 and55 and between signal transmitting line 33 and 54.

In an alternative configuration, the logical circuit 50 may be part of alogical pre-coder (not shown), for example of the type commonly used inthe art to encode DMPSK signals.

In use, an optical radiation impinges on the modulator 20 at its opticalinput 21. The optical radiation may be generated by an optical source(not shown), e.g. a distributed feedback (DFB) semiconductor laser orexternal cavity laser (ECL) or a narrow linewidth laser suitable fortelecommunication applications (FWHM<10 MHz). The optical radiation maybe a continuous wave radiation or a modulated radiation. For example, ina typical RZ transmission configuration, the optical radiation may be astream of optical pulses having a duty cycle and a clock rate, or pulserate, and may be obtained by an RZ optical shaper (not shown). The RZshaper can be any intensity modulator, including electroabsorptionmodulators or single-drive Mach-Zehnder modulators. Optionally, theoptical shaper may be integrated with, or placed at, the output of themodulator 20. The modulator 20 phase-modulates the optical radiation inorder to generate at the optical output 22 an MPSK optical signal. Thefirst driver 30 and the second driver 31 drive the modulator by using afirst and a second drive voltage signal, respectively V₁ and V₂. Each ofthe two drivers 30, 31 receives a respective logical signal, S₁ and S₂,through the respective transmitting lines 32 and 33. The drive voltagesignals V₁, V₂ depend upon the respective logical signals S₁ and S₂. Forthe purpose of the present invention, an optical device such as amodulator or a phase-shifter will be regarded as driven equivalently bythe drive voltage signals (e.g. V₁,V₂) or by the respective logicalsignals (e.g. S₁ and S₂). In an exemplary configuration, when themodulator is a QPSK modulator, the signals S₁ and S₂ are typicallybinary and the signals V₁ and V₂ are typically two level voltagesignals. In a typical configuration, for example in case of a DMPSKtransmission, the logical signals are generated by a pre-coder (notshown) using known techniques. Preferably, the two (RF) logical signalsare independent from each other. Each two-level voltage signal drivesone arm of the interferometric modulator 60, which allows applying adifferent phase change in each of the arms. A careful synchronization,for example by way of RF electrical phase shifters, between the twological signals at the input of the first and the second driver isadvantageous in order to obtain the desired undistorted M-level phasemodulated signal.

In a preferred configuration wherein the modulator 60 is a MZM, thefield transfer function of the modulator 60 can be written, withoutconsidering attenuation and chirping, as $\begin{matrix}{E_{o} = {{E_{in}\left( {{\cos\quad\phi_{d}} - {j\frac{1}{{ER}_{lin}}s\quad{\mathbb{i}n}\quad\phi_{d}}} \right)}{\mathbb{e}}^{j\quad\phi_{s}}}} & (2)\end{matrix}$

wherein E₀ is the optical field at the output 22 of the modulator 60,E_(in) is the optical field at the input 21 of the modulator 60 andER_(lin) is the (linear) Extinction Ratio. In the above expression, usehas been done of the following notation: $\left\{ \begin{matrix}{\phi_{d} = \frac{\phi_{1} - \phi_{2}}{2}} \\{\phi_{s} = \frac{\phi_{1} + \phi_{2}}{2}}\end{matrix} \right.$

wherein φ₁ and φ₂ are the phase-shifts applied to the optical radiationtraversing respectively the first and second arm 63, 64.

In a more preferred configuration wherein the modulator 20 is a DD-MZM,phase-shifts φ₁ and φ₂ are related to respective driving voltages V₁ andV₂ according to the relation: φ_(j)=πV_(l)/V_(π) (i=1,2), where V_(π) isDD-MZM modulator π voltage.

It is remarked that in the special case of a 2-level 0-π phasemodulation, not contemplated by the present invention, the added phasevanishes (φ_(s)=0) and φ_(d) is 0 or π according to the input signal.Equation (1) reduces to E_(o)=E_(in) cos φ_(d) and the extinction ratiodoes not affect the transmitted 0-π constellation.

Equation (2), by neglecting the second term of the right-hand side, i.e.in the presence of an ideal MZM having an infinite extinction ratio,reduces to:E _(o) =E _(in) cos φ_(d) e ^(jφ) ^(s)   (3)

In table 1 an exemplary set of phases φ_(s) and φ_(d) is shown as afunction of the applied voltages, V₁ and V₂, for an exemplary QPSKsignal generated by a DD-MZM modulator. The right-most column shows thecorresponding transmitted phase symbol φ_(sym) in the constellation ofFIG. 1. Also shown is an exemplary set of binary logical signals S₁ andS₂, which determine the driving voltages. The specific relationshipbetween V_(1,2) and S_(1,2) is arbitrary. TABLE 1 φ_(sym) (QPSK phase S₁S₂ V₁ V₂ φ₁ φ₂ φ_(d) φ_(s) symbol) 0 1 0 1/2 V_(π) 0 +π/2 −π/4 +π/4 +π/40 0 0 −1/2 V_(π) 0 −π/2 +π/4 −π/4 −π/4 1 1 V_(π) 1/2 V_(π) +π +π/2 +π/4+3/4 π +3/4 π 1 0 V_(π) −1/2 V_(π) +π −π/2 +3π/4 +π/4 −3/4 π

In the ideal case of an infinite ER, applying the proper phase shifts(φ₁ and φ₂) to arms 63 and 64 it is possible to obtain a constant outputoptical amplitude and the four-level phase constellation correspondingto the QPSK modulation format shown in FIG. 1.

In order to ensure phase quadrature between the two phase-shifts φ₁ andφ₂, a proper control of the modulator bias or drive voltages V₁ and V₂is preferred, e.g., by means of well-known techniques (e.g. feedbackcircuit).

Applicant has found that when using an interferometric modulator, havingan extinction ratio ER, the RF-ER causes a distortion of the MPSK phaseconstellation with respect to the desired MPSK constellation. In fact,due to the ER of the modulator, a phase deviation φ_(e) is added to theconstellation. The value of the phase deviation φ_(e) is computed as:$\begin{matrix}\begin{matrix}{\phi_{e} = {{arc}\quad{{tg}\left( \frac{{Im}\left( E_{o} \right)}{{Re}\left( E_{o} \right)} \right)}}} \\{= {{arc}\quad{{tg}\left( {- \frac{\sin\quad\phi_{d}}{{ER}_{lin}\cos\quad\phi_{d}}} \right)}}} \\{= {{arc}\quad{{{tg}\left( {- \frac{{tg}\quad\phi_{d}}{{ER}_{lin}}} \right)}.}}}\end{matrix} & (4)\end{matrix}$

The term tg(φ_(d)) is equal to +1 or −1, due to the fact that when theoutput field intensity in (3) is kept constant, φ_(d) is π/4±nπ/2(n=1,2,3) and the phase deviation alternatively adds or subtracts to thedesired phase levels.

In table 2 the phases, φ_(1,2), φ_(s,d) and φ_(sym) and the phase errorφ_(e) are shown as a function of the driving voltages V₁ and V₂ in theparticular case of table 1: TABLE 2 φ_(sym) (phase V₁ V₂ φ₁ φ₂ φ_(s)φ_(d) symbol) φ_(e) 0 1/2 V_(π) 0 +π/2 +π/4 −π/4 +π/4 +|φ_(e)| 0 −1/2V_(π) 0 −π/2 −π/4 +π/4 −π/4 −|φ_(e)| V_(π) 1/2 V_(π) +π +π/2 +3/4π +π/4+3/4π −|φ_(e)| V_(π) −1/2 V_(π) +π −π/2 +π/4 3/4π −3/4π +|φ_(e)|

In FIG. 3 it is shown the degraded QPSK constellation of FIG. 1 due tothe finite ER of the interferometric QPSK modulator. Blank circlesrepresent the desired constellation, filled circles the distortedconstellation.

As an example, when using the distorted QPSK constellation of table 2for DQPSK transmission, the modulator ER causes phase distances (Δ)among the transmitted phase symbols to be different from pre-selectedvalues 0, +π/4, +π and −π/2. As is clear from FIG. 3 and table 2. thedistorted DQPSK constellation is 0, +π/2±|φ_(e)|, +π and −π/2±|φ_(e)|.

At the unbalanced Mach-Zehnder receiver, according to (1), the detectedsignal is no more binary, but six different current levels aregenerated. FIG. 4 a shows an output current after the balancedphotodetector for the desired DQPSK constellation and FIG. 4 b shows anoutput current after the balanced photodetector for the distorted DQPSKconstellation.

Applicant has found that it is possible to counteract the phasedistortion due to the ER by applying a proper phase-shift to the MPSKoptical signal outputting from the modulator 20. The MPSK optical signaloutputting from the modulator 20 impinges on the device 40, which issuitable to selectively apply a phase-shift φ_(c) to the optical phaseof the MPSK optical signal. Advantageously, the phase contribution to beapplied is selected on a symbol-by-symbol basis. Preferably the appliedphase-shift is approximately constant over the symbol period T, beingcontemplated that a possible transient between successive symbols doesnot depart from the phase-shift being approximately constant. Morepreferably, the applied phase-shift has a sign, which is selectivelydetermined symbol-by-symbol as a function of the symbol phase value.Even more preferably, the applied phase-shift has a magnitude, which isa function of ER. The phase-shift magnitude is advantageously the samefor substantially all the optical symbols generated by the modulator 20.

The sign of the phase-contribution to be applied is determined on asymbol-by-symbol basis in dependence on the phase value of thetransmitted optical symbol. It is in general convenient to find alogical relation which gives the sign of the phase-contribution as afunction of the logical signals (e.g. S₁, S₂) feeding the drivers (e.g.30, 31) of the modulator 20. A general method suitable to find thelogical relationship comprises the step of building a table with all thetransmitted phase symbol values in dependence of all the possible valuesof the logical signals and with the phase distortions associated to eachphase symbol value. Using known synthesis techniques, it is possible tofind the logical relationship and to build a suitable logical circuit 50implementing the resulting relation.

As an example, in case of a QPSK transmission, from tables 1 and 2 it ispossible to derive the logical relationship: NOT[XOR (S₁,S₂)], where S₁and S₂ are the binary logical signals in input to the drivers 30,31driving the two arms 63,64 of the modulator 60, XOR is the logicaloperation EXCLUSIVE OR and NOT is the logical INVERSION. The result ofthe algorithm determines the sign of the phase contribution: a logical“1” will correspond to a positive phase contribution, a logical “0” to anegative phase contribution.

Exemplarily, FIG. 5 shows a logical representation of a particularembodiment of a logical circuit 50 suitable to implement a logicalrelationship NOT[XOR (S₁,S₂)] valid for an exemplary QPSK transmission,in which a same reference numeral is assigned to elements having thesame functionality. Logical blocks 70 represent logical splitters,blocks 71 represent inverters, blocks 72 represent AND gates and block73 represents OR gate. Advantageously, no use has been done of XORgates. In this case, signals S₁ and S₂ feed the two input ports 52 and51, respectively.

An output logical signal S₃ is generated at the output 53, whereinS₃=NOT[OR(S₁ AND (NOT(S₂)), (NOT(S₁)) AND S₂)], which is equivalent toNOT[XOR (S₁,S₂)]. The logical signal S₃ is directed to driver 44 throughthe signal transmitting line 56.

In an alternative configuration, the logical operation giving the signof the above phase-shift may be performed directly by a suitablepre-coder, such as for example a pre-coder for a DMPSK transmission. Inthis case the logical circuit 50 can be integrated in said precoder andit may derive the logical signal determining the sign of the phase-shiftto the driver 44 of the phase shifter 40 directly from the original datastreams feeding the precoder, without making use of the logical signalsfeeding the modulator (e.g. S₁ and S₂). In this case, an equivalentrelation will be valid between the original data streams and the logicalsignal to the driver 44 and the logical circuit 50 will be designedaccording to it. In any case, the logical signal to the driver 44 andthe logical signals to the modulator (e.g. S₁ and S₂) will be linked bythe same relation of the previous embodiment

Advantageously, the phase shifter 40 applies the phase-shift φ_(c) whosemagnitude, from (4), is substantially given by: $\begin{matrix}{{\phi_{c}} = {{{arc}\quad{{tg}\left( \frac{1}{{ER}_{lin}} \right)}} \approx {\frac{1}{{ER}_{lin}}.}}} & (5)\end{matrix}$

Table 3 (derived from (5)) shows different values of the phasecorrection as a function of different modulator extinction ratios. Itcan be seen that for currently typical commercially available MZMs, thenecessary phase contribution is equal to or less than about 16°, orequivalently equal to or less than about π/10. The phase shifter 40,which is driven by the driver 44, does not require high drive voltages(V₃). TABLE 3 ER |φ_(c)| |φ_(c)| (dB) (deg) (rad) 11 15.7° 0.27 12 14.1°0.25 13 12.6° 0.21 14 11.3° 0.19 15 10.1° 0.17

By way of comparison, FIGS. 6, 7 and 8 report the simulated optical eyediagrams of an exemplary DQPSK signal at 10 Gsymbol/s generated by anon-ideal DD-MZM transmitter and back-to-back received by a couple ofunbalanced MZ interferometers in the case of different values of theDD-MZM ER (FIG. 6 a and FIG. 6 b: ER=20 dB, FIG. 7 a and FIG. 7 b: ER=15dB, FIG. 8 a and FIG. 8 b: ER=12 dB). Simulations are performed with aDD-MZM electrical bandwidth of 20 GHz and by making use of the circuitryof FIG. 5 for phase correction. A laser line-width of 2 MHz, atransmitter bandwidth of 20 GHz and a noisy electrical receiver (NEP=15pW/sqrt(Hz)) with 10.5 GHz bandwidth were the other simulationparameters.

In the figures on the left the eye diagrams obtained with the DD-MZMalone are shown, while on the right the eye diagrams obtained inpresence of the phase shifter correction are shown. The phase correctionsuitably induced by the phase shifter improves the eye opening, almosteliminating the distortion due to finite ER.

Tables 4 and 5 summarize performance improvements when applying thepresent invention, in terms of Q factor enhancement and eye openingrecovery. Eye opening values are compared to the bottom line, where asufficiently high value of ER (ER=500 dB) simulates the ideal case ofinfinite ER. Simulations demonstrate that by applying the presentinvention also to a 12 dB extinction ratio DD-MZM it is possible toovercome the performance of a 20 dB ER MZM. TABLE 4 Q w/o phasecorrection Q w/ phase correction RF Extinction Ratio [dB] [dB] [dB] 128.71 18.41 15 11.66 20.12 20 16.28 22.88 500 25 25

TABLE 5 Eye opening without Eye opening with phase RF Extinction Ratio[dB] phase correction correction 12 0.276 0.79 15 0.52 0.85 20 0.750.943 500 1 1

An advantage of the invention is the relaxation of the constraints on ERwhen manufacturing interferometric modulators, such as DD-MZM.

In the following, it is described the case of an MPSK signal having M=8,as an example of application of the present invention to multileveloptical phase signal modulation with more than M=4 levels. Referencenumerals of FIG. 2 will be used whenever appropriate. By employing aDD-MZM 60 and by driving the two electrodes 65, 66 with multilevelelectrical signals V₁, V₂ having the condition of a π/2 bias point, i.e.the difference between the two voltage signals is equal to about 1/2V_(π), it is possible to obtain an 8-level PSK modulated signal. Thecondition of a π/2 bias point is equivalent to the condition that thephase difference between the phase-shifts φ₁, φ₂ applied to the opticalradiation traversing respectively the first and second arm 63, 64 isequal to about π/2. Table 6 shows an exemplary set of values of signalsV₁ and V₂ and the corresponding transmitted phase symbol φ_(sym), whennot considering the MZM's ER (ideal DD-MZM). TABLE 6 V₁ 1/4 V_(π) 1/2V_(π) 3/4 V_(π) V_(π) 5/4 V_(π) 3/2 V_(π) 7/4 V_(π) 2 V_(π) V₂ −1/4V_(π) 0 1/4 V_(π) 1/2 V_(π) 3/4 V_(π) V_(π) 5/4 V_(π) 3/2 V_(π)φ_(sym (8-PSK)) 0 π/4 π/2 3/4π π 5/4π 3/2π 7/4π

When considering the finite value of modulator's ER, a phase deviationφ_(e) is added to the constellation according to equation (4), which isvalid independently from the number of levels M. The induced impairmentover the transmitted signal is even higher than the one over a 4-levelQPSK signal, because the transmitted phase symbols have a closer phasedistance from each other. To recover the correct constellation aphase-shifting device 40 can be employed. The amount of phase the device40 should add or subtract depends on the MZM's ER according to equation(5). The sign of the phase corrections, and consequently the correctionalgorithm, can be obtained from the table of the effectively transmittedphase symbols.

In a preferred configuration, the apparatus comprising the modulator 20and the phase shifter 40 is optically integrated, optionally in amonolithic structure, possibly also integrating an optical source.Advantages of this preferred configuration are its compact-size and thefact that it remains more insensitive to environmental perturbation thana non-integrated solution, e.g. a fiber-based solution. In case themodulator 60 is a DD-MZM, it does not need any stabilization controlloop, its structure being optically integrated.

The inventive apparatus can be very easily adjusted to ensure it workswith different DD-MZM extinction ratios, by simply varying thephase-shifter driving voltage (V₃). In this way it is unnecessary toprovide MZM 60 with an exact ER when transmitters have to be produced inquantity, reducing discard rate.

The present invention also contemplates any combination of MPSK or DMPSKwith any other modulation technique, such as intensity (IM) or amplitudemodulation (ASK) or polarization shift keying (POLSK).

The present invention finds particularly advantageous applications inany combination of the MPSK or DMPSK formats with any multiplexingtechnique, such as wavelength division multiplexing (WDM) orpolarization division multiplexing (PoIDM).

In fact MPSK is able to increase the data transmission spectralefficiency by a factor of N with respect to OOK transmission andmoreover it has been shown a high robustness towards strong opticalfiltering, thus allowing a closer allocation of adjacent optical channelin a DWDM optical system.

1-15. (canceled)
 16. A method for modulating optical radiation,comprising the steps of: phase-modulating the optical radiation with amodulation signal, by using a modulator, so as to obtain a multi-levelphase shift key optical signal comprising a stream of optical pulses,wherein each of said optical pulses has a respective optical phase valuerelated to said modulation signal; and applying to each of said opticalpulses a phase-shift having an absolute value and a sign related, foreach of the optical pulses, to said respective optical phase value. 17.The method of claim 16, wherein said phase-shift is substantiallyconstant in each of said optical pulses.
 18. The method of claim 16,wherein the absolute value of said phase-shift is equal to or less thanabout π/10.
 19. The method of claim 16, wherein said modulator has anextinction ratio and the absolute value of said phase-shift isdetermined as a function of said extinction ratio.
 20. The method ofclaim 16, wherein the absolute value of said phase-shift is equal toabout ${{arc}\quad{{tg}\left( \frac{1}{{ER}_{lin}} \right)}},$ whereinER_(lin) is the extinction ratio.
 21. The method of claim 16, furthercomprising the steps of: providing a first and a second logical signal(S₁, S₂) linked with said modulation signal; generating a first and asecond driving signal for said modulator from said first and secondlogical signal; and establishing said sign as a logical function of saidlogical signals.
 22. The method of claim 21, wherein said logicalfunction is equivalent to NOT[XOR(S₁,S₂)].
 23. The method according toclaim 16, wherein said multilevel phase shift key optical signal is adifferential multilevel phase shift key optical signal.
 24. A method ofoptical communication comprising transmitting an optical signal at afirst location and receiving the optical signal at a second locationdifferent from the first location, wherein transmitting comprisesmodulating the optical signal by performing at least steps of:phase-modulating the optical signal with a modulation signal, so as toobtain a multi-level phase shift key optical signal comprising a streamof optical pulses, wherein each of said optical pulses has a respectiveoptical phase value related to said modulation signal; and applying toeach of said optical pulses a phase-shift having an absolute value and asign related, for each of the optical pulses, to said respective opticalphase value.
 25. An electro-optical apparatus for modulating opticalradiation based on a modulation signal, comprising: an optical modulatorcapable of receiving optical radiation and generating a multilevel phaseshift key optical signal including a stream of optical pulses, eachhaving a respective optical phase value related to said modulationsignal, said optical modulator being capable of being driven by a firstand a second driving signal (S₁, S₂); a phase-shifter opticallyconnected to the optical modulator, capable of applying to the phase ofeach optical pulse a phase-shift having an absolute value and a signdepending, for each of the optical pulses, on said respective opticalphase value; and a logical circuit capable of generating a third drivingsignal (S₃) logically related to said first and second driving signals,the logical circuit being logically connected to the phase-shifter forfeeding said third driving signal to said phase-shifter.
 26. Theapparatus according to claim 25, wherein said third driving signal (S₃)determines said sign of said phase shift.
 27. The apparatus according toclaim 25, wherein said optical modulator comprises a dual-driveMach-Zehnder modulator.
 28. The apparatus according to claim 25, whereinsaid optical modulator is an optical modulator capable of receivingoptical radiation and generating a quadrature phase shift key opticalsignal.
 29. An optical transmitter comprising an optical sourceoptically coupled to an electro-optical apparatus for modulating opticalradiation based on a modulation signal, the electro-optical apparatuscomprising: an optical modulator capable of receiving optical radiationand generating a multilevel phase shift key optical signal including astream of optical pulses, each having a respective optical phase valuerelated to said modulation signal, said optical modulator being capableof being driven by a first and a second driving signal (S₁, S₂); aphase-shifter optically connected to the optical modulator, capable ofapplying to the phase of each optical pulse a phase-shift having anabsolute value and a sign depending, for each of the optical pulses, onsaid respective optical phase value; and a logical circuit capable ofgenerating a third driving signal (S₃) logically related to said firstand second driving signals, the logical circuit being logicallyconnected to the phase-shifter for feeding said third driving signal tosaid phase-shifter.
 30. An optical communication system comprising anoptical transmitter for transmitting an optical signal, an opticalreceiver for receiving the optical signal, and an optical communicationline connecting the transmitter to the receiver, wherein the transmittercomprises an electro-optical apparatus for modulating optical radiationbased on a modulation signal, the electro-optical apparatus comprising:an optical modulator capable of receiving optical radiation andgenerating a multilevel phase shift key optical signal including astream of optical pulses, each having a respective optical phase valuerelated to said modulation signal, said optical modulator being capableof being driven by a first and a second driving signal (S₁, S₂); aphase-shifter optically connected to the optical modulator, capable ofapplying to the phase of each optical pulse a phase-shift having anabsolute value and a sign depending, for each of the optical pulses, onsaid respective optical phase value; and a logical circuit capable ofgenerating a third driving signal (S₃) logically related to said firstand second driving signals, the logical circuit being logicallyconnected to the phase-shifter for feeding said third driving signal tosaid phase-shifter.
 31. The method according to claim 19, wherein saidfunction is a decreasing function with increasing said extinction ratio.32. The apparatus according to claim 25, wherein said third drivingsignal (S₃) is logically related to said first and second drivingsignals (S₁, S₂) through the logical relationship NOT[XOR(S₁,S₂)].